Limit theorems for random permanents with exchangeable structure

Journal of Multivariate Analysis

Volumn 91, Issue 2, 2004, Pages 224-239

  Rempała, Grzegorz A ^a,b   Wesołowski, Jacek ^c  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF LOUISVILLE   (United States)

^c WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Central limit theorem; Orthogonal expansion; Random permanent

Indexed keywords

EID: 4344619457     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmva.2004.01.003     Document Type: Article

References (25)

1. Avram F. Taqqu M.S. Symmetric polynomials of random variables attracted to an infinitely divisible law Probab. Theory Related Fields 71 4 1986 491-500
2. Billingsley P. Convergence of Probability Measures 1999 Wiley New York
3. J.P.M. Binet, Memoire sur un systeme de formules analytiques, et leur application à des considérations géometriques. [Memoirs on the System of Analytic Formulae and Their Application to Geometric Considerations.], L' École Politechnique, Paris, France, 1812.
4. Borovskikh Y.V. Korolyuk V.S. Random permanents and symmetric statistics Acta Appl. Math. 36 3 1994 227-288
5. Chow Y.S. Teicher H. Independence, interchangeability, martingales, Probability Theory 1978 Springer New York
6. Coelho M.P. Duffner M.A. On the relation between the determinant and the permanent on symmetric matrices Linear Multilinear Algebra 51 2 2003 127-136
7. Feige U. Lund C. On the hardness of computing the permanent of random matrices Comput. Complexity 6 2 1996/97 101-132
8. Forbert H. Marx D. Calculation of the permanent of a sparse positive matrix Comput. Phys. Comm. 150 3 2003 267-273
9. Girko V.L. Theory of random determinants in: Mathematics and its Applications (Soviet Series) Vol. 45 1990 Kluwer Academic Publishers Group Dordrecht
10. Janson S. The numbers of spanning trees, Hamilton cycles and perfect matchings in a random graph Combin. Probab. Comput. 3 1 1994 97-126
11. V.S. Korolyuk, Y.V. Borovskikh, Random permanents and symmetric statistics, in: A.N. Shiryaev (Ed.), Probability Theory and Mathematical Statistics (Kiev, 1991), World Scientific Publishing, River Edge, NJ, 1992, pp. 176-187.
12. Lee A.J. U-statistics. Theory and practice Statistics: Textbooks and Monographs Vol. 110 1990 Marcel Dekker Inc. New York
13. Pate T.H. The best lower bound for the permanent of a correlation matrix of rank two Linear Multilinear Algebra 51 3 2003 263 -278
14. Rempała G. Asymptotic behavior of random permanents Random Oper. Stochastic Equations 4 1 1996 33-42
15. Rempała G., Wesołowski J. Asymptotic behavior of random permanents Statist. Probab. Lett. 45 1999 149-158
16. Rempała G., Wosołowski J. Central limit theorems for random permanents with correlation structure J. Theoret. Probab. 15 1 2002 63-76
17. Rempała G., Wesołowski J. Incomplete U-statistics of permanent design J. Nonparametr. Statist. 15 2 2003 221-236
18. Rubin H. Vitale R.A. Asymptotic distribution of symmetric statistics Ann. Statist. 8 1 1980 165-170
19. H.J. Ryser, Combinatorial Mathematics, The Mathematical Association of America, New York, 1963.
20. Székely G.J. A limit theorem for elementary symmetric polynomials of independent random variables Z. Wahrsch. Verw. Gebiete 59 3 1982 355-359
21. G.J. Székely, L. Szeidl, On the limit distribution of random permanents, in: A.V. Skorokhod, V. Borovskikh, (Eds.) Exploring Stochastic Laws, VSP, Utrecht, 1995, pp. 443-455.
22. Taylor R.L. Daffer P.Z. Patterson R.F. Limit Theorems for Sums of Exchangeable Random Variables 1985 Rowman & Allanheld Publishers Totowa, NJ
23. Teicher H. Distribution and moment convergence of martingales Probab. Theory Related Fields 79 2 1988 303-316
24. Valiant L.G. The complexity of computing the permanent Theoret. Comput. Sci. 8 2 1979 189-201
25. van Es A.J. Helmers R. Elementary symmetric polynomials of increasing order Probab. Theory Related Fields 80 1 1988 21-35